Bertrand Russell, on his "On Denoting", states that “the father of Charles II was executed” becomes
“It is not always false of x that x begat Charles II and that x was executed and that ‘if y begat Charles II, y is identical with x’ is always true of y”.
This last sentence is logically expressed as ¬(∀x)[¬(Bx∧Ex∧(∀y)[By⊃(y=x)])], which is logically equivalent to (∃x)[Bx∧Ex∧(∀y)[By⊃(y=x)]]. But this sentence is false, since the third part of the conjunction ((∀y)[By⊃(y=x)]) is false. And (∀y)[By⊃(y=x)] is false because there is an y such that y begat Charles II and y≠x. In this case, y is the mother of Charles II, who begat him and wasn't executed.

Is my analysis correct? For me, his 'translation' for "the father of Charles II was executed" doesn't have enough predicates to distinguish x from other things, and since there is more than one thing that begat Charles II, he would need to predicate another characteristic to confer uniqueness to x.
A solution for this would be consider "It is not always false of x that x begat Charles II and that x was executed and that x was a man and that ‘if y begat Charles II and y was a man, y is identical with x’ is always true of y". That is ¬(∀x)[¬(Bx∧Ex∧Mx∧(∀y)[By∧My⊃(y=x)])]. This is true, because although there are more than one thing that begat Charles II, there is only one which begat him and that is a man.

What do you think?